Which graph among the following is a velocity-time straight-line graph, that describes a person's motion if he runs with uniform acceleration for the first 10 seconds, walks with constant speed for the next 10 seconds, and slowly decreases his speed to arrive at his destination for the final 10 seconds.

The slope of the velocity-time graph represents the object's acceleration in motion. A straight line slope indicates uniform acceleration, whereas a curved slope indicates variation in acceleration during motion, i.e. non-uniform acceleration. For a straight-line slope, a positive slope indicates acceleration, while a negative slope indicates retardation. 

According to the question, the graph for the first 10 seconds when he runs with uniform acceleration should be a straight line with a positive slope, then for the next 10 seconds when he walks with constant velocity, the graph should be a straight line parallel to the x-axis as the slope becomes zero for constant velocity, and finally for the final 10 seconds when he slowly decreases his velocity, implying negative acceleration, i.e. retardation. 

Therefore, this is the right graph.